Andrew factored the expression 20x^3-12x^2+8x as 4x (5x^2-12x^2+8x). But when Melissa applied the distributive law and multiplied out 4x (5x^2-12x^2+8x), she got 20x^3-48x^3+32x^2; thus, Andrew’s solution does not appear to check. Why is that? Please help Andrew to understand this better. Explain your reasoning and correctly factor the original expression, if possible. If the expression is prime, so state.
sure, you can take 4x out but do it properly
4x (5 x^2 -3 x + 2)
Use the discriminant to determine whether the following equations have solutions that are: two different rational solutions; two different irrational solutions; exactly one rational solution; or two different imaginary solutions.
x2 = 3x – 6
Andrew made a mistake while factoring the expression. Let's analyze where he went wrong.
Andrew started by factoring out 4x from the expression 20x^3-12x^2+8x as 4x (5x^2-12x^2+8x). However, the mistake occurred when he simplified the expression inside the parentheses.
Instead of subtracting the exponents, Andrew mistakenly subtracted the coefficients. That is why he got 20x^3-48x^3+32x^2.
To correctly factor the expression, we need to group the terms appropriately.
The original expression is:
20x^3 - 12x^2 + 8x
First, let's factor out the greatest common factor. In this case, it is 4x. Divide each term of the expression by 4x:
4x(5x^2 - 3x + 2)
Now, we have a trinomial inside the parentheses. We need to see if it can be factored further.
The trinomial 5x^2 - 3x + 2 cannot be factored using integers or simple factors. So, the factored form of the original expression is:
4x(5x^2 - 3x + 2)
This expression cannot be factored any further, and it is not considered prime because it has a common factor of 4x.
Therefore, the correct factored form of the original expression is 4x(5x^2 - 3x + 2).